Some Studies On Euler-poisson Equations

The Euler-Poisson equations are used to describe the motion of fluids with the electric force or self-gravitating force. The force is governed by a Poisson equation. There are two typical models. One is to model the flow of electron in semiconductor devices or plasma. The other one describes self-gravitating flows.In this thesis, we first introduce some results on transonic shock solutions for the Euler-Poisson equations in semiconductor devices. Second, we study the existence of transonic shock solutions of self-gravitating Euler-Poisson equations. We proved the existence and uniqueness of one dimensional transonic shock solutions if the boundary conditions are prescribed in the upstream. We also give a perspective for spherical symmetrical problems for the Euler-Poisson equations.